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# Common Core Standard HSA-REI.C.5 Questions

Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

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Grade 9 Linear Equations CCSS: HSA-REI.C.5
Solve the system of equations.
$-x+y=3$
$x+y=7$
1. x=3, y=1
2. x=2, y=5
3. x=1, y=1
4. x=4, y=2
5. x=5, y=2
Grade 9 Linear Equations CCSS: HSA-REI.C.5
Solve the system of equations.
$x+3y=9$
$4x-2y=-6$
1. x=0, y=0
2. x=3, y=7
3. x=1, y=2
4. x=3, y=3
5. x=0, y=3
Grade 10 Linear Equations CCSS: HSA-REI.C.5
Select the solution to the system of linear equations.
$x+y=8$
$2x-y=1$
1. $(5, 2)$
2. $(2/5, 2/11)$
3. $(2, 5)$
4. $(3, 5)$
Grade 10 Linear Equations CCSS: HSA-REI.C.5
Grade 10 Linear Equations CCSS: HSA-REI.C.5
Select the solution to the system of linear equations.
$t+2s=1$
$2t-3s=23$
1. $s=-3, t=7$
2. $s=2/3, t=2$
3. $s=-3/7, t=1/3$
4. $s=-7, t=3$
Grade 10 Linear Equations CCSS: HSA-REI.C.5
Select the solution to the system of linear equations.
$r=-3s$
$r+4s=10$
1. $r=-30, s=10$
2. $r=3/4, s=-3/4$
3. $r=1/3, s=3$
4. No Solution
Grade 10 Linear Equations CCSS: HSA-REI.C.5
Select the solution to the system of linear equations.
$x+2y=11$
$3x-2y=9$
1. $(3, 2)$
2. $(5, 3)$
3. $(4.5, 2)$
4. $(1/2, 2/3)$
Grade 10 Linear Equations CCSS: HSA-REI.C.5
Select the solution to the system of linear equations.
$y=5x+8$
$4y+x=4$
1. $(-4,3)$
2. $(1,2)$
3. $(-4/3,4/3)$
4. $(1/2,2/5)$
Grade 11 Linear Equations CCSS: HSA-REI.C.5
Grade 11 Linear Equations CCSS: HSA-REI.C.5
Grade 11 Linear Equations CCSS: HSA-REI.C.5
Grade 11 Linear Equations CCSS: HSA-REI.C.5
Grade 11 Linear Equations CCSS: HSA-REI.C.5
Grade 11 Linear Equations CCSS: HSA-REI.C.5
Grade 11 Linear Equations CCSS: HSA-REI.C.5
Grade 11 Linear Equations CCSS: HSA-REI.C.5
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